STA 312 Fall 2010 Categorical Data Analysis (Discrete random variables)

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Presentation transcript:

STA 312 Fall 2010 Categorical Data Analysis (Discrete random variables)

Vitamin C and Colds ColdNo Cold Placebo31109 Vitamin C17122

Race of Prisoner and Victim White VictimBlack Victim White Prisoner151 9 Black Prisoner 63103

Graduate School Admissions Not AdmittedAdmitted Dept. A Dept. B Dept. C Dept. D Dept. E Dept. F668 46

Issues to consider Sometimes there is a clear independent variable and dependent variable, sometimes not -- different statistical models? Of course some variables have more than 2 categories. Beyond 2-dimensions (Prisoner race by Victim race by Death penalty, Admission by Sex by Department) Structural zeros - Sex by Cause of death, but one cause is childbirth.

Two treatments for Kidney Stones Treatment ATreatment B Effective273 (78%)289 (83%) Ineffective7761 Total350

Simpson’s Paradox Treatment ATreatment B Small Stones93% (81/87)87% (234/270) Large Stones73% (192/263)69% (55/80) Both78% (273/350)83% (289/350)

Distributions Bernoulli Binomial Multinomial Poisson (process)

Poisson Process Events happening randomly in space or time Independent increments For a small region or interval, –Chance of 2 or more events is negligible –Chance of an event roughly proportional to the size of the region or interval Then (solve a system of differential equations), the probability of observing x events in a region of size t is